Whether solid or laminated, curved wood articles used for handrails, stringers, furniture parts and the like traditionally have been made by various methods, namely, by cutting, milling and steam bending.
However, the manufacture of compound curved wooden workpieces presents entirely different technical problems than a simple curved workpiece.
Examples of "compound" curved workpieces are handrails for a staircase wherein the handrails extend upwardly in a generally spiral or helical fashion. In this case, it will be appreciated that each handrail as a whole not only "curves" upwardly around a vertical axis, but also that the hand or palm surface also changes its orientation as the handrail curves upwardly in order to present a holding surface for a person going up or down the stairs.
Spiral and helical structures are only two types of shapes that fall within the genus "compound curve". In a broader sense, a compound curve may be explained as follows.
If one imagines a rectangular three dimensional form in space, it can be said that it has a height h, width w and length l. Further, it has a longitudinal axis lx and a vertical axis v which is at 90 degrees to the plane generated by extending the longitudinal axis. That is, the plane generated by extending the lx axis may be considered as extending between 90 degrees and 270 degrees and the plane generated by extending the v axis thus extends from 0 degrees to 90 degrees.
Further, in the above construct, it is postulated that the lx plane is parallel to the top and bottom surfaces of the rectangular structure, and the v plane is parallel to the sides of such structure.
Having this geometric form in mind, a workpiece is placed at the front wall of the rectangle and positioned so that its lengthwise axis is coincident with axis lx and so that its vertical axis is coincident with axis v.
However, as the workpiece is moved into the rectangle, because it has a compound curve, its lengthwise axis lw is non linear. Accordingly, as each finite section enters the rectangle, the lw axis along that portion of the workpiece diverges from axis lx. This divergence may be up or down from either side of lx.
Similarly, the horizontal planar axis hw of workpiece also diverges from the horizontal planar axis hx of the rectangle, i.e., it rotates around plane hx in order to conform to the rotation of the planar axis lw around the axis v, in order to maintain the side walls parallel to the top walls of the workpiece. In other words, axis hw diverges from the v axis.
The above, of course, is susceptible of expression in purely mathematical fashion, but it is thought that the more general verbal description given is advantageous. Moreover, while the foregoing example utilizes a rectangular workpiece, articles having compound curves may be, wholly or partly, oval, circular or have many other cross-sectional shapes. Moreover, the cross-sectional shapes may change from one section of the workpiece to another.
In one important of the embodiment of the invention described herein, the workpiece is a handrail which is rectangular in cross-section from one end to the other.
As the handrail is formed so that its lengthwise and horizontal axes, follow (or generate) a compound curve, it is important for many applications that the rectangular shape be preserved, i.e., at any given cross-section along lw, that the top and bottom surfaces of the handrail be parallel, and that the opposing sides be parallel and at 90 degrees to the top and bottom surfaces.
Thus, in connection with such a handrail, it has a compound curve, i.e., as the vertical axis vw of the handrail changes orientation, its horizontal axis hw also changes in orientation by the same amount to preserve the rectangular shape of the handrail at every cross-section.
To produce a compound curve workpiece, it may be possible to do so by utilizing a highly controlled (e.g., computer controlled) saw or other cutting device, but this technique requires a rigorous layout in the form of a detailed engineering design and a complex computer program. Even if this could be accomplished, it would require a great deal of time. It would also involve starting with a large block of wood and thus there would be extensive waste, which is costly. Conceivably, such a handpiece could also be fashioned by manual cutting, but the operator would have to be highly skilled and it is not realistic to expect that such manual expertise would be consistent enough to produce the same end product--which is what is required not only for mass production, but also for custom applications.
On the other hand compound curve articles are desirable for a variety of applications, including handrails, stringers, furniture parts and other items, and it is important that any system used be repeatable, so that mass production is possible.
While it is possible to form a compound curve article such as a handrail on a forming frame from a solid piece of wood, for purposes of efficiency and to be able to provide highly complex shapes, it is practically necessary to form the workpiece from a plurality of laminates. More specifically, glue is applied to both surfaces of laminate strips and, prior to the setting of the glue, and when the laminates can still move with respect to each other, the entire assembly is clamped about a forming frame in the shape of a compound curve. The glue then dries while the workpiece is held to the frame, so that the compound curve shape of the workpiece is set.
However, while the use of laminates as described has significant advantages, there is always sideways slippage of individual lamina. Consequently, the sides of the workpiece are rough since individual lamina protrude by different amounts.